The One-Degree Error – Why Tennis Is So Difficult

Feb 15

You’ve probably heard and definitely experienced that tennis is a difficult sport.

Hitting a moving ball with a moving racquet while you are moving into a rather small target – assuming you’re not aiming in the middle of the court – is not that easy.

To really illustrate the point, ask yourself this question:

How much will you miss your intended target if your racquet’s angle is just one degree off?

This tennis infographic below will hopefully answer this questions and also tell you how accurate your timing must be and how you need to adjust your technique of hitting through the ball in order to avoid missing by so much.

tennis infographic

So next time when you miss the court by less than 41 cm (1.35 feet), know that you made an error of less than one degree on your racquet which was probably a result of mistiming your shot by less than one hundredth of a second.

Do you really need to get down on yourself after missing a shot or can you perhaps be more understanding see that it’s not always your fault but that the game of tennis is somewhat difficult…

P.S. If you know a physicist or a mathematician, please share this post them and ask them to contribute their thoughts to it.

(Note to webmasters: feel free to embed this infographic on your tennis blog and help your readers understand the difficulties of the game of tennis.)

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(17) comments

Arturo Hernandez February 15, 2014


Great post!

It is remarkable that people can hit the ball at all into such a small space given such great error. And yet people don’t miss by that much despite all these obstacles. This suggests that our ability to hit balls to very specified targets is difficult and that we must be extra careful when moving, hitting down the line or hitting very flat. So I guess tennis is all about building as much cushion as possible. My sense is that this margin is improved a lot by topspin and the use of newer materials in rackets and strings. I feel like the possibility of getting the ball in is much higher than it was 10 years ago and even higher than it was 20 years ago. Is that your sense? Arturo

    Tomaz February 15, 2014

    Hi Arturo,

    Yes, the new strings and lighter racquets make it possible to apply massive amounts of topspin and keep the ball in the court easier – but of course, one must work on accelerations a lot to achieve that.

    Joe March 14, 2014

    In addition the topspin, the margin of error is increased because the racket is not moving through the hitting zone like the hands of a clock. If the racket head is square to the ball for 6 inches then you don’t have to be perfect.

Oscar Tanhueco February 15, 2014

Excellent, sound advice.

steve February 15, 2014

HI Tomaz

I find that the problem with playing tennis is this fixation with hitting the ball instead of watching the ball and being focused on having the racquet in the right place before you swing, watching where the ball is going, getting your body in the right position and have all your concentration on the contact point then get ready if the ball is coming back.

    Tomaz February 15, 2014

    No doubt, many more challenges besides finding the right angle of the racquet of course.

Misha Sakharoff February 15, 2014

Thanks Tomaz, very inspiring!

I thought about the same but related to the serving motion.

It could be interesting to show how much the up-spring from the trophy pose in order to meet the ball as high as possible would contribute to the chance of hitting inside the service box. Sharper/flatter service angle diminish you chances to hit the narrow space between the net and service line of your opponent. Higher contact point instantly gives bigger chances to hit right. Distance between your body vertical axis and the contact point changes the angle too.

Wouldn’t it be interesting to show how much a cm shift of contact point (horizontal/vertical) contributes to chances of hitting an ace?


    Tomaz February 15, 2014

    Yes, Misha, that’s another interesting math equation that could help answer the question why so many serves end up in the net.

    Let me know when that’s posted on your blog. 😉

Robert February 15, 2014

As I read through this I thought of the age-old advice to aim to give yourself a margin of about a yard or meter in from sidelines and the baseline. That accounts that degree of deviation plus some. And who said that Trig class wouldn’t come in handy in the future!

Rafael Vital Jr. February 16, 2014

Being that a very small deviation in racket head angle and/or timing error, can result in missing your target or even the entire court, you will start to appreciate the use of good technique, good practice, and many hours of competition as a way of playing more with your subconscious mind (getting in the zone) and less with your conscious or critical mind!!


Frercks Hartwig February 16, 2014

Thanks Tomaz!

This is a phantastic argument for “trick your mind-” or “Inner Coaching-Drills”. I’ve posted your article on my blog May be this is an addition to your article:

Greetings vom Germany,


[…] Bij het recreatief researchen van allerlei tennisgerelateerde zaken sprong er vandaag 1 artikel in het bijzonder voor mij uit. Dit artikel, van, behandelt een zeer wiskundige kant van het tennis – al zul je niet heel veel concrete wetenschappelijke conclusies kunnen trekken. […]

Amar May 2, 2014

If one were to use the mirror (your racquet) and light ray (the ball)model, every one degree of deviation in the plane of the racquet (represented by the mirror) will cause a two degree deviation in the path of the ball (represented by the reflected ray path). In effect the difficulty is double of what you have stated!!!
I take this opportunity to propose a thought on hitting the ball.
Hitting the ball can be represented the the laws of collision in physics. In a perfectly elastic collision momentum (the product of mass and velocity) is conserved. Simplifying things one can also say when two objects travelling in exactly opposite directions (example the ball and racquet)collide then in an ideal situation they exchange momentum.
Taking the analogy further you can consider the player and racquet as one system colliding with the ball.
On the average we can say a player is about 1000 times heavier than the ball. In effect if the player moves towards the incoming ball at say 3 KM/Hr (a very easy walking pace) and manages just a 5% efficient collision the ball will travel back at a surprising 150 KM/Hr.
What I am proposing is if we concentrate on a forward body weight movement and just bring the racquet forward to meet the ball in as elastic a way as possible (loose easy hands, racquet face square…….) trying to feel our momentum going into the ball we may be able to create a very powerful hit with little or no effort.
On the other hand the arm and racquet as a system are perhaps about 100 times heavier than the ball. Following the principle of conservation of momentum and when you consider that I have assumed just 5% efficiency of collision, there is far more potential in trying to learn how to make a more efficient hit rather than a powerful “arm ” hit.
Your thoughts please.

    Tomaz May 2, 2014

    Excellent, Amar. I understand what you’re saying because I feel it. 😉

    I actually feel moving my center of gravity just that little bit forward while hitting the ball and feeling that I go with my weight against the ball.

    Since contact lasts just 3-5 thousands of a second, my weight transfer move lasts very short time and I also move very little – but more than enough to put my weight against the ball in that short moment of contact.

    So yes, you’re right about, but of course it requires exquisite timing and attention to detail to pull it off. I probably takes years to master, at least I am aware of how much I have fine tuned that process, but again, very good to know what the ultimate goal is.

    Thanks again, very good explanation.

      Amar May 4, 2014

      Yes Tomaz, When you consider every degree of deviation in the racquets plane angle will alter the ball position by 80cm at the base line then creating a hit by meeting the ball with a forward body movement and not swinging at the ball takes an even greater significance.
      I am working hard in this direction and there are days when I get it, but almost into the sixth decade of life things are ephemeral like the morning mist.
      Thanks for reinforcing my belief.


[…] because even a small change in the racquet head angle creates a big change in where the ball lands on the other side, this solution creates a very […]


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